My first thought was that there were 99 such pairs but then I noticed the conditions that $x\ne y$ and that order is not to be considered. Dropping the pair (50, 50) leave 98 pairs and half of that is 49.

Yes, there are 49. The positive integer pairs, (x, y), such that x+ y= 100 are (1, 19)

Typo. This was, of course, supposed to be (1, 99).

Quote:

, (2, 98 ), (3, 97), ... (97, 3), (98, 2), (99, 1).

My first thought was that there were 99 such pairs but then I noticed the conditions that $x\ne y$ and that order is not to be considered. Dropping the pair (50, 50) leave 98 pairs and half of that is 49.